lecture note 4 - C2M2 Rational Fractions or Partial...

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C2M2 Rational Fractions or Partial Fraction Decompositions When you were learning basic algebra there were probably problems assigned on adding fractions which had constants, linear expressions, and quadratic expressions in x in the numerators and denominators. Our objective here is to take the answers to those questions and Fnd the fractions that were added together. The need here is to break down a complicated fraction into several simple ones whose anti-derivatives are (much!) easier to Fnd. To approach this systematically we separate the problems into groups determined by the nature of the denominators of the fractions. Recall that P ( x )= x 2 a 2 can be factored into P ( x )=( x a )( x + a ), so we say that P ( x )i s reducible . Likewise, Q ( x x 2 + a 2 can NOT be factored, so Q ( x s irreducible . There are di±erent approaches to to these problems and we will use substitution as our method. Two principles from algebra are applicable here. The Frst states that if two polynomials in x agree for all values of x , then the polynomials have the same coefficients, that is, they are identical. The second states that x r is a factor of the polynomial P ( x ) if and only if P ( r )=0.
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This note was uploaded on 04/08/2008 for the course MATH 1112 taught by Professor Iacob during the Spring '08 term at Georgia Southern University .

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lecture note 4 - C2M2 Rational Fractions or Partial...

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